I'll say $\vec{a}$ and $\vec{b}$ are collinear if they lies in same line, like (1, 2, 3) and (-1, -2, -3). What should I call two vectors in same direction but with different lengths? like (1, 2, 3) and (2, 4, 6). (Of course they are collinear, but is there any more specific term for them?)
$\endgroup$ 22 Answers
$\begingroup$You can say (1,2,3) and (2,4,6) are parallel.
As $ \vec{a} = k \vec{b}$
Edit - Difference between parallel and collinear
If two parallel vectors have angle = 0 between them that is both are in same direction but collinear vector lie in same plane they may be parallel or anti parallel that is angle = 180.
$\endgroup$ 3 $\begingroup$The proper term is that one vector is a positive scalar multiple of the other. Or you could say that they give the same normalised vector (which is the vector obtained by dividing them by their own length). In a more informal discussion you could say the vectors point in the same direction.
$\endgroup$ 1
